package leetcode.editor.cn;

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

/**
 * @id: 37
 * @title: 解数独
 */
 
//编写一个程序，通过填充空格来解决数独问题。 
//
// 数独的解法需 遵循如下规则： 
//
// 
// 数字 1-9 在每一行只能出现一次。 
// 数字 1-9 在每一列只能出现一次。 
// 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。（请参考示例图） 
// 
//
// 数独部分空格内已填入了数字，空白格用 '.' 表示。 
//
// 
//
// 
// 
// 
// 示例： 
//
// 
//输入：board = [["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5","."
//,".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".","."
//,"3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"
//],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],["
//.",".",".",".","8",".",".","7","9"]]
//输出：
// [["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"
//],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["
//4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","
//6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","
//5","2","8","6","1","7","9"]]
//解释：输入的数独如上图所示，唯一有效的解决方案如下所示：
//
//
// 
//
// 
//
// 提示： 
//
// 
// board.length == 9 
// board[i].length == 9 
// board[i][j] 是一位数字或者 '.' 
// 题目数据 保证 输入数独仅有一个解 
// 
// 
// 
// 
// Related Topics 数组 回溯 矩阵 
// 👍 1072 👎 0

public class P37SudokuSolver {
    public static void main(String[] args) {
        Solution solution = new P37SudokuSolver().new Solution();
        // todo
        char[][] b = new char[][]{
                {'5', '3', '.', '.', '7', '.', '.', '.', '.'},
                {'6', '.', '.', '1', '9', '5', '.', '.', '.'},
                {'.', '9', '8', '.', '.', '.', '.', '6', '.'},
                {'8', '.', '.', '.', '6', '.', '.', '.', '3'},
                {'4', '.', '.', '8', '.', '3', '.', '.', '1'},
                {'7', '.', '.', '.', '2', '.', '.', '.', '6'},
                {'.', '6', '.', '.', '.', '.', '2', '8', '.'},
                {'.', '.', '.', '4', '1', '9', '.', '.', '5'},
                {'.', '.', '.', '.', '8', '.', '.', '7', '9'}
        };
        solution.solveSudoku(b);
        for (int i = 0; i < b.length; i++) {
            for (int j = 0; j < b[i].length; j++) {
                System.out.print(b[i][j] + " ");
            }
            System.out.println("");
        }
    }
    
//leetcode submit region begin(Prohibit modification and deletion)
class Solution {
     // DFS 递归回调
    int[][] rows = new int[9][9];
    int[][] clus = new int[9][9];
    int[][] palaces = new int[9][9];
    boolean end = false;
    List<int[]> blanks = new ArrayList<>();
    public void solveSudoku(char[][] board) {
        // TODO 先预处理，得到rows和clus和palaces，和空格位置
        for (int i = 0; i < 9; ++i) {
            for (int j = 0; j < 9; ++j) {
                if (board[i][j] != '.') {
                    int palaceNo = (i / 3) * 3 + (j / 3);
                    int idx = board[i][j] - '0' - 1;
                    rows[i][idx] += 1;
                    clus[j][idx] += 1;
                    palaces[palaceNo][idx] += 1;
                } else {
                    blanks.add(new int[]{i, j});
                }
            }
        }
        solve(board, 0);
    }

    private void solve(char[][] board, int pos) {
        if (pos == blanks.size()) {
            end = true;
            return;
        }
        // 获取空格的位置
        int[] blank = blanks.get(pos);
        int x = blank[0];
        int y = blank[1];
        int palaceNo = (x / 3) * 3 + (y / 3);
        List<Integer> canUse = marge(rows[x], clus[y], palaces[palaceNo]);
        for (int idx : canUse) {
            if (end) {
                return;
            }
            boolean isValid = rows[x][idx] == 0 || clus[y][idx] == 0 || palaces[palaceNo][idx] == 0;
            if (isValid) {
                board[x][y] = (char) ('0' + idx + 1);
                rows[x][idx] += 1;
                clus[y][idx] += 1;
                palaces[palaceNo][idx] += 1;
                // 下一层
                solve(board, pos + 1);
                // 回溯回来上一个空格要重试其他的数字
                // 恢复现场
                rows[x][idx] -= 1;
                clus[y][idx] -= 1;
                palaces[palaceNo][idx] -= 1;
                board[x][y] = '.';
            }
        }
    }

    private List<Integer> marge(int[] row, int[] clu, int[] palace) {
        List<Integer> result = new ArrayList<>();
        for (int i = 0; i < 9; ++i) {
            if (row[i] + clu[i] + palace[i] == 0) {
                result.add(i);
            }
        }
        return result;
    }
}
//leetcode submit region end(Prohibit modification and deletion)


}